Drillstring Pressure Losses
All pressure losses, at first, assume a laminar flow regime. Power Law Model calculations begin with:
where: Plf = Pressure Loss in Laminar Flow (psi)
L = Length of Section (feet)
VP = Velocity in Section of drill string (ft/min)
d = Inside Diameter of drillstring (inches)
k = Consistency Index
n = Power Index
Fluid velocity in the drillstring can be determined by using:
where: Q = Pump flow rate (gpm)
d1 = pipe I.D. (inches)
The equivalent viscosity (m) is then determined, using:
Which, in turn, is used to determine the Reynolds Number.
Flow behavior, with the Power Law Model, will vary depending on the “n” value of the fluid. The critical Reynolds Number (Rec) is found using: 3470 - 1370n (from laminar to transitional)
4270 - 1370n (from transitional to turbulent)
If: Re < Rec flow is laminar
Re is between laminar and turbulent, flow is transitional
Re > Rec flow is turbulent
If the flow is determined to be turbulent, the pressure losses will have to be re-calculated using turbulent flow. This will also require a friction factor (f) to be included:
